机器学习 之 贝叶斯分类（上）

   虽然是个菜鸟，但是决定好好研究一下机器学习算法，初步决定 一周学习两种算法，希望我能坚持下来！此过程中难免出错，望各位前辈指出探讨！同时文章可能借鉴其他博客书籍等资料，请海涵！

   第一篇选择贝叶斯分类，因为它是比较基础的一种机器学习算法。今天介绍简单理论和R的简单实现。

  朴素贝叶斯法是基于贝叶斯定理与特征条件独立假设的分类方法。算法的基础是概率问题，分类原理是通过某对象的先验概率，利用贝叶斯公式计算出其后验概率，即该对象属于某一类的概率，选择具有最大后验概率的类作为该对象所属的类。

朴素贝叶斯两个假设：①特征间独立 （各个特征出现与否与其他特征无关）

                                         ② 每个特征同等重要

   但朴素贝叶斯算法简单，快速，具有较小的出错率。

假设有数据D，我们由一组数据D导出一个参数化模型M=M(ω).

计算方法：

                                       

P(M): 先验概率

P(M|D) 后验概率

则 问题转化为  已知数据D求模型M的概率为后验概率。

贝叶斯推断方法：比较两个特定模型的后验概率P（M1|D）和P（M1|D）来比较这两个模型。后验概率值越大，相应的误差越小。（MAP估计，最大后验概率估计）  常用的先验分布:高斯分布，伽马分布和Dirichlet分布

若假定所有参数具有均匀的先验分布（P(M)）,求较大P(M|D)问题（MAP最大后验概率估计）即转化为求最大P(D|M)问题（ML最大似然估计）。

为了便于比较，通常取对数进行计算。

【参考文献1】贝叶斯分类 主要 对于输入特征x，利用通过学习得到的模型计算后验概率分布，将后验概率最大的分类作为输出。
根据贝叶斯定理，后验概率P(Y=cx | X=x) = 条件概率P(X=x | Y=cx) * 先验概率P(Y = ck) / P(X=x)，取P(X=x | Y=cx) * P(Y = ck)最大的分类作为输出。

R简单贝叶斯分类R简单贝叶斯分类

[plain] view plaincopy#构造训练集  data <- matrix(c("sunny","hot","high","weak","no",                   "sunny","hot","high","strong","no",                   "overcast","hot","high","weak","yes",                   "rain","mild","high","weak","yes",                   "rain","cool","normal","weak","yes",                   "rain","cool","normal","strong","no",                   "overcast","cool","normal","strong","yes",                   "sunny","mild","high","weak","no",                   "sunny","cool","normal","weak","yes",                   "rain","mild","normal","weak","yes",                   "sunny","mild","normal","strong","yes",                   "overcast","mild","high","strong","yes",                   "overcast","hot","normal","weak","yes",                   "rain","mild","high","strong","no"), byrow = TRUE,                 dimnames = list(day = c(),                 condition = c("outlook","temperature",                   "humidity","wind","playtennis")), nrow=14, ncol=5);    #计算先验概率  prior.yes = sum(data[,5] == "yes") / length(data[,5]);  prior.no  = sum(data[,5] == "no")  / length(data[,5]);    #模型  naive.bayes.prediction <- function(condition.vec) {      # Calculate unnormlized posterior probability for playtennis = yes.      playtennis.yes <-          sum((data[,1] == condition.vec[1]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(outlook = f_1 | playtennis = yes)          sum((data[,2] == condition.vec[2]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(temperature = f_2 | playtennis = yes)          sum((data[,3] == condition.vec[3]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(humidity = f_3 | playtennis = yes)          sum((data[,4] == condition.vec[4]) & (data[,5] == "yes")) / sum(data[,5] == "yes") * # P(wind = f_4 | playtennis = yes)          prior.yes; # P(playtennis = yes)        # Calculate unnormlized posterior probability for playtennis = no.      playtennis.no <-          sum((data[,1] == condition.vec[1]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(outlook = f_1 | playtennis = no)          sum((data[,2] == condition.vec[2]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(temperature = f_2 | playtennis = no)          sum((data[,3] == condition.vec[3]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(humidity = f_3 | playtennis = no)          sum((data[,4] == condition.vec[4]) & (data[,5] == "no"))  / sum(data[,5] == "no")  * # P(wind = f_4 | playtennis = no)          prior.no; # P(playtennis = no)            return(list(post.pr.yes = playtennis.yes,              post.pr.no  = playtennis.no,              prediction  = ifelse(playtennis.yes >= playtennis.no, "yes", "no")));  }    #预测  naive.bayes.prediction(c("rain",     "hot",  "high",   "strong"));  naive.bayes.prediction(c("sunny",    "mild", "normal", "weak"));  naive.bayes.prediction(c("overcast", "mild", "normal", "weak")); 

 

最后一个分类预测结果如下：

$post.pr.yes[1] 0.05643739$post.pr.no[1] 0$prediction[1] "yes"

参考网址：

1、http://blog.csdn.net/yucan1001/article/details/23033931

2、机器学习实战 Peter Harrington著 

下节将会介绍贝叶斯在文本分类应用的实例。